Exam 5: Discrete Probability Distributions

A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the Student will pass the test? Round to three decimal places.

Use the given values of n=2112, $p = \frac { 3 } { 4 }$ to find the minimum value that is not significantly low, $\mu - 2 \sigma$ and the maximum value that is not significantly high, $\mu + 2 \sigma$ Round your answer to the nearest hundredth unless otherwise noted.

Multiple-choice questions on a test each have 5 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions. a. Use the multiplication rule to find the probability that the first 2 guesses are wrong and the last 3 guesses are correct. That is, find P(WWCCC), where C denotes a correct answer and W denotes a wrong answer. b. Make a complete list of the different possible arrangements of 2 wrong answers and 3 correct answers, then find the probability for each entry in the list. c. Based on the preceding results, what is the probability of getting exactly 3 correct answers when 5 guesses are made?

A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is Independent of the others.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 53 times, keeping track of the "fives" rolled.

In a recent U.S. Open tennis tournament, among 20 of the calls challenged by the players, 8 were overturned after a review using an electronic system. Assume that when players challenge calls, they are successful in having them overturned 50% of the time. The probability that among 20 challenges, 8 or fewer are overturned is 0.252. Does this result suggest that the success rate is less than 50%? Why or why not?

On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of Correct answers.

In a survey sponsored by Coca-Cola, subjects aged 15-65 were asked what contributes most to their happiness. The table is based on their responses. Determine whether a probability distribution is given and two reasons why or why not. Contributes Most to Happiness ( ) Family 0.77 Friends 0.15 Work/Study 0.08 Leisure 0.08 Music 0.06 Sports 0.04

An experiment consists of rolling a single die 12 times and the variable x is the number of times that the outcome is 6. Can the Poisson distribution be used to find the probability that the outcome of 6 occurs exactly 3 times, why or why not?

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. ( ) 0 0.109 1 0.208 2 0.246 3 0.159 4 0.096 5 0.228

Find the standard deviation, $\sigma$ , for the binomial distribution with n=38 and p=0.4 .

The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 0.4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than 0.4 ounces? Consider as significant any result that differs from the mean by more than 2 standard deviations. That is, significant values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$

Find the mean, $\mu$ for the binomial distribution which has the stated values of n and p . Round answer to the nearest tenth. n=676 ; p=0.7

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. ( ) 1 0.14 2 0.16 3 0.12 4 0.14 5 0.13 6 0.31

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 26 times, keeping track of the numbers that are rolled.

In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest To:

The braking time of a car. Identify the given random variable as being discrete or continuous.

In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 Belong to an ethnic minority? Round to three decimal places.

Based on a USA Today poll, assume that 10% of the population believes that college is no longer a good investment. Find the probability that among 16 randomly selected people, at least 1 believes that college is no longer a good investment.

Assume that a procedure yields a binomial distribution with a trial repeated n = 30 times. Use the binomial probability formula to find the probability of x = 5 successes given the Probability p = 1/5 of success on a single trial. Round to three decimal places.